ZLAEV2(3)      LAPACK routine of NEC Numeric Library Collection      ZLAEV2(3)



NAME
       ZLAEV2

SYNOPSIS
       SUBROUTINE ZLAEV2 (A, B, C, RT1, RT2, CS1, SN1)



PURPOSE
            ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
               [  A         B  ]
               [  CONJG(B)  C  ].
            On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
            eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
            eigenvector for RT1, giving the decomposition

            [ CS1  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
            [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].




ARGUMENTS
           A         (input)
                     A is COMPLEX*16
                    The (1,1) element of the 2-by-2 matrix.

           B         (input)
                     B is COMPLEX*16
                    The (1,2) element and the conjugate of the (2,1) element of
                    the 2-by-2 matrix.

           C         (input)
                     C is COMPLEX*16
                    The (2,2) element of the 2-by-2 matrix.

           RT1       (output)
                     RT1 is DOUBLE PRECISION
                    The eigenvalue of larger absolute value.

           RT2       (output)
                     RT2 is DOUBLE PRECISION
                    The eigenvalue of smaller absolute value.

           CS1       (output)
                     CS1 is DOUBLE PRECISION

           SN1       (output)
                     SN1 is COMPLEX*16
                    The vector (CS1, SN1) is a unit right eigenvector for RT1.






FURTHER DETAILS
             RT1 is accurate to a few ulps barring over/underflow.

             RT2 may be inaccurate if there is massive cancellation in the
             determinant A*C-B*B; higher precision or correctly rounded or
             correctly truncated arithmetic would be needed to compute RT2
             accurately in all cases.

             CS1 and SN1 are accurate to a few ulps barring over/underflow.

             Overflow is possible only if RT1 is within a factor of 5 of overflow.
             Underflow is harmless if the input data is 0 or exceeds
                underflow_threshold / macheps.



LAPACK routine                  31 October 2017                      ZLAEV2(3)